What is time complexity of Linked List operations?

The time complexity of various operations on linked lists can vary depending on the type of linked list (singly, doubly, or circular) and the specific operation being performed. Here is a detailed breakdown of the time complexities for common operations on linked lists:

Singly Linked List

Insertion

• At the beginning: $$O(1)$$ - This operation involves updating the head pointer to the new node, which is a constant-time operation[2][3][7].
• At the end: $$O(n)$$ - This requires traversing the entire list to find the last node, making it a linear-time operation[3][7].
• At a given position: $$O(n)$$ - This involves traversing the list to the desired position, which takes linear time[3][7].

Deletion

• At the beginning: $$O(1)$$ - This operation involves updating the head pointer to the next node, which is a constant-time operation[2][3][7].
• At the end: $$O(n)$$ - This requires traversing the entire list to find the second-to-last node, making it a linear-time operation[3][7].
• At a given position: $$O(n)$$ - This involves traversing the list to the desired position, which takes linear time[3][7].

Access/Search

• Access by index: $$O(n)$$ - Accessing an element by index requires traversing the list from the head to the desired position, which takes linear time[3][7].
• Search for an element: $$O(n)$$ - Searching for an element involves traversing the list until the element is found, which takes linear time[3][7].

Traversal

• Traversal: $$O(n)$$ - Traversing the entire list to visit each node takes linear time[3][7].

Doubly Linked List

Insertion

• At the beginning: $$O(1)$$ - This operation involves updating the head pointer and the previous pointer of the old head node, which is a constant-time operation[2][3][7].
• At the end: $$O(1)$$ - This operation involves updating the tail pointer and the next pointer of the old tail node, which is a constant-time operation[2][3][7].
• At a given position: $$O(n)$$ - This involves traversing the list to the desired position, which takes linear time[3][7].

Deletion

• At the beginning: $$O(1)$$ - This operation involves updating the head pointer and the previous pointer of the new head node, which is a constant-time operation[2][3][7].
• At the end: $$O(1)$$ - This operation involves updating the tail pointer and the next pointer of the new tail node, which is a constant-time operation[2][3][7].
• At a given position: $$O(n)$$ - This involves traversing the list to the desired position, which takes linear time[3][7].

Access/Search

• Access by index: $$O(n)$$ - Accessing an element by index requires traversing the list from the head or tail to the desired position, which takes linear time[3][7].
• Search for an element: $$O(n)$$ - Searching for an element involves traversing the list until the element is found, which takes linear time[3][7].

Traversal

• Traversal: $$O(n)$$ - Traversing the entire list to visit each node takes linear time[3][7].

Circular Linked List

Insertion

• **At the beginn...